SOLUTION: Please present this in a mathematical sentence.
1. A motorcycle driver travels 15kph faster than a bicycle rider. The motorcycle driver covers 60 km in two hours less than the tim
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Question 878737: Please present this in a mathematical sentence.
1. A motorcycle driver travels 15kph faster than a bicycle rider. The motorcycle driver covers 60 km in two hours less than the time it takes the bicycle rider to travel the same distance? please present it step by step... thank you for helping.
2. A garden 7m by 12m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92m^2. please present it step by step... thankyou for helping.
God bless
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. A motorcycle driver travels 15kph faster than a bicycle rider.
The motorcycle driver covers 60 km in two hours less than the time it takes the bicycle rider to travel the same distance?:
Let s = the bike speed
then
(s+15) = the motorcycle speed
Write a time equation; time = dist/speed
Bike time - M'cycle time = 2hr
- = 2; Sorry for the mistake here!
multiply eq by s(s+15) cancel the denominators and you have
60(s+15) - 60s = 2s(s+15)
60s + 900 - 60s = 2s^2 30s
Combiner as a quadratic equation on the left
0 = 2s^2 + 30s - 900
simplify divide by 2
s^2 + 15s - 450 = 0
Factors to
(s+30)(s-15) = 0
the positive solution
s = 15 km/hr is the bike speed
then
30 km/hr is M'cycle speed
:
Check this by finding the time of each
60/15 = 4 hrs
60/30 = 2 hrs
--------------
differ: 2 hrs
:
;
2. A garden 7m by 12m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92m^2
:
Let x = the width of the border
Find the area of the garden 7*12 = 84 sq/m
Find the total area of the garden and the border: 84 + 92 = 176 sq/m
:
The overall length and width will be 2x greater the the garden's
(2x+7)(2x+12) = 176
Foil
4x^2 + 24x + 14x + 84 = 176
4x^2 + 38x + 84 - 176 = 0
4x^2 + 38x - 92 = 0
Factors to
(2x + 23)(2x-4) = 0
The positive solution
2x = 4
x = 2 m is the width of the border
:
:
Check this , find the area of the overall dimensions + 4m
11 * 16 = 176
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Number 1 item could be analyzed by filling a data table for rate, time, distance; the question is a uniform rates for travel type.
r = speed for bicycle
t = time for bicycle
__________________speed___________time_________distance
motorcycle________r+15____________t-2__________60
bicycle____________r_______________t___________60
The number 1 item does not actually contain a question; it only contains a description. No matter, because you specified that you want a mathematical sentence. RT=D for rate, time, distance. The rate unit is kilometers per hour. You can first form TWO equations:
-
(r+15)(t-2)=60
and
rt=60
-
How much more do you need from that?
, using substitution with the other equation
Which do you want to finish solving first? t or r ?
My choice..... using the second equation again, ,
-
, just divided both sides by 15.
, just multiplied both sides by t.
Use the general solution of a quadratic formula, and select the meaningful result for t. Use it to solve for r.
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